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Numbers and Numerals: A Weekend Exploration
Part 2. Sunday
Rhea was helping her brother water the garden plants when Dhruv rang the doorbell.
D: Hey Rhea! Any luck with our cryptic clue yet?
R (frowning): Did you come in here for that?
D (grinning): Just thought I’d come say hi. After all,...
R: Hmm, cut it out! To answer your question, no. Still thinking.
D: I was wondering if we can figure this out, together. I was thinking about this last night. We could begin by trying to understand what the word even means. What is an even number?
R: A number with last digits 0, 2, 4, 6, or 8.
D: Right. But, since Anu ma’am said that we should try and think of it without using the concept of numerals, let’s avoid using this digit-based definition.
R: I really don’t understand what that means. What is the difference between numbers and numerals? Aren’t they the same thing?
D: Hmm, let’s look up ‘numeral’ in the dictionary.
R: Oxford Dictionary gives this meaning of ‘numeral’: “a figure, symbol, or group of figures or symbols denoting a number.” Oh, I think I got...!! (appears suddenly confused). Wait, no! I thought I had figured it out, but I guess not.
D: I think I’m beginning to get it. But I’m unable to describe what I’m thinking. Never mind, let’s have lunch and we’ll ask Anu Ma’am on Monday.
A flash of light and a loud clang! Dhruv looked around him, not remotely surprised, but mildly annoyed. Rhea turned towards the source of the sound and panicked.
R: Oh my god, what is that?
D: Umm, you mean ‘who is that’? That’s Socrates. He keeps showing up. Apparently whenever he feels I’m giving up, he jumps in. I found it really entertaining at first, but sometimes it's a little annoying.
S: Hello Dhruv! It is I, Socrates.
D: Yes, yes, I know! I always know.
S: But you can never be sure!
D (rolls eyes): He always does this.
R: But this is great, Dhruv! Maybe Socrates can help us. Socrates, what’s the difference between numbers and numerals?
S: Rhea, that’s not what I’m here for. I never give away the answers. But I can give you a clue.
R: Alright, a clue then!
S: Let’s look at it this way. How do you write 2 in Hindi?
Rhea drew the symbol on the board: २
S: That’s right. How about Roman 2?
Dhruv drew another symbol on the board: II
S: So, what do 2, २, and II have in common?
R: Umm, they all mean the same thing.
D: And I guess this ‘same thing’ is the ‘number’. Is that what Anu Ma’am was talking about, Socrates? Socrates? Hellloooo??!
In their excitement, they hadn’t noticed that Socrates was gone!
D (laughing): He always leaves when I get back on track. Ok, now, I’m really hungry!
Pause and Reflect:
How does this renewed understanding of numbers and numerals help you understand why Anu ma’am found the proof the class was discussing to be trickery.